$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x - 8$ and $ BC = 2x + 2$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x - 8} = {2x + 2}$ Solve for $x$ $ 5x = 10$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({2}) - 8$ $ BC = 2({2}) + 2$ $ AB = 14 - 8$ $ BC = 4 + 2$ $ AB = 6$ $ BC = 6$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {6} + {6}$ $ AC = 12$